# Events for 01/25/2023 from all calendars

## Noncommutative Geometry Seminar

**Time: ** 2:00PM - 3:00PM

**Location: ** BLOC 302

**Speaker: **Shiqi Liu, Penn State

**Title: ***Analysis of the hypoelliptic Laplacian*

**Abstract: **Invented by Jean-Michel Bismut, the hypoelliptic Laplacian is the centerpiece of a new type of index theory. It leads to a remarkable trace formula and reveals completely new insights into geometry and representation theory. However, the subject relies on analysis that is made difficult by the non-ellipticity of the hypoelliptic Laplacian operator. Recently, with techniques from noncommutative geometry, we have shown that the hypoelliptic Laplacian is actually elliptic under a new calculus. This will significantly reduce the complexity of the analysis.
This is joint work with N. Higson, E. MacDonald, F. Sukochev, and D. Zanin.

## Groups and Dynamics Seminar

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Nataliya Goncharuk, Texas A&M University

**Title: ***Renormalization operators and Arnold tongues*

**Abstract: **Many studies in circle dynamics are devoted to rotation numbers of circle maps, and to so-called Arnold tongues: level sets of rotation numbers in parametric families of circle maps. In particular, E.Risler proved in 1999 that irrational (Diophantine) Arnold tongues in analytic families of circle diffeomorphisms are analytic. In contrast to this result, Llave and Luque observed in 2011 using numerical investigations that Arnold tongues are only finitely smooth near critical circle maps. With M.Yampolsky, we provided explanations of these effects in terms of renormalization operators.